Buridan's donkey
A hungry donkey stands exactly halfway between two identical bales of hay. With no reason to prefer either, a perfectly rational donkey would starve.
- Reading time
- 4 min
- Difficulty
- Introductory
- Branch
- Decision
- First posed
- Named after Jean Buridan, 14th century, though the puzzle appears in Aristotle, On the Heavens, and in Al-Ghazali
The puzzle
A donkey is hungry and thirsty in equal measure, or, in the more common version, hungry and placed exactly halfway between two bales of hay. The bales are identical in size, quality and smell. The donkey has no reason whatsoever to prefer one to the other.
If the donkey always acts on the strongest reason, it has no reason to go left rather than right. So it stays where it is, and starves to death between two meals.
The puzzle is named after the fourteenth-century French philosopher Jean Buridan, though the donkey does not appear in his surviving writings; it seems to have been invented by his critics to mock his views about the will. Versions are much older. Aristotle mentions a man equally hungry and thirsty, placed between food and drink. Al-Ghazali, in the eleventh century, described a man choosing between two identical dates, and used the case to argue that the will can choose without a reason.
Why it matters
The donkey tests what we mean by rational choice and by free will. If a choice must always follow from reasons, then in perfectly balanced cases no choice is possible, yet we pick between identical options constantly: two cans of soup, two seats on a train.
It also has a surprising afterlife in engineering, where a version of the problem, called the arbiter or metastability problem, affects the design of digital circuits that must decide between two inputs arriving at almost exactly the same time.
Key terms
- Principle of sufficient reasonThe principle, championed by Leibniz, that everything that is the case has a reason or explanation why it is so and not otherwise.
- Liberty of indifferenceA will's supposed power to choose between options when it has no reason to prefer either, as in Buridan's donkey.
- Free willThe capacity to choose between options in a way that makes us the real authors of our actions and responsible for them. What exactly that requires is the central dispute.
- MetastabilityIn electronics, an unstable in-between state a circuit can get stuck in when two inputs arrive almost simultaneously and it must decide between them. A real-world cousin of Buridan's donkey.
Proposed solutions
The will can choose without reason
The will has the power to pick between equal options. This shows that choice is not just the mechanical result of the strongest motive.
There is always a tiebreaker
Perfect balance never really occurs. Some tiny asymmetry always decides the matter.
Choose arbitrarily: it is rational
When options are equally good, it is rational to pick either, or to randomise. Doing nothing is the irrational choice.
Each solution, tested
The will can choose without reason
- How it resolves the paradox
- Al-Ghazali argued that a person faced with two identical dates simply takes one; the will can single out one option where reason cannot. He used this to argue that God's will could choose a particular moment for creation without needing a reason to prefer it. Defenders of liberty of indifference see the case as evidence for a will that is more than a balance scale.
- Why it doesn’t fully work
- Critics such as Ibn Rushd (Averroes) replied that there is always some small difference, in position, in perception, which tips the balance. The will is not choosing without reason; we just fail to notice the reason.
There is always a tiebreaker
- How it resolves the paradox
- Gottfried Wilhelm Leibniz, committed to the principle of sufficient reason, held that nothing happens without a reason why it is so and not otherwise. In a real world, two bales can never be perfectly identical, nor a donkey perfectly centred. Some imperceptible difference will always tip the choice. If perfect balance did occur, the donkey would indeed not move.
- Why it doesn’t fully work
- This seems to concede that a perfectly rational agent could be paralysed in principle, and makes our ability to choose depend on luck.
Choose arbitrarily: it is rational
- How it resolves the paradox
- The donkey's situation contains a third option, starving, which is far worse than either bale. Rationality does not require a reason to choose this bale over that one; it requires a reason to choose a bale over none, which is overwhelming. Picking arbitrarily, or flipping a coin, is the rational response to a tie. Edna Ullmann-Margalit and Sidney Morgenbesser called this 'picking' as opposed to 'choosing'.
- Why it doesn’t fully work
- This works for ties, but the paradox reappears in a deeper form: how does the agent pick, if nothing favours either option? Something has to break the symmetry, and that something is not a reason.
Who argued what
- The will can choose without reason Al-Ghazali, Duns Scotus
- There is always a tiebreaker Gottfried Wilhelm Leibniz, Ibn Rushd (Averroes), Baruch Spinoza
- Choose arbitrarily: it is rational Edna Ullmann-Margalit, Sidney Morgenbesser
Variations
The circuit
A digital circuit must decide whether a signal arrived before or after a clock tick. If the two arrive at almost exactly the same moment, the circuit can hang in an in-between state for an unpredictably long time. Leslie Lamport called this 'Buridan's principle': a discrete decision based on a continuous input cannot always be made within a bounded time. Engineers manage it with careful design, but cannot eliminate it.
The career
Two job offers are, after long reflection, equally good. Weeks pass while you agonise. Is endless deliberation a failure of rationality, or its excess? Many people eventually flip a coin and notice, as it spins, which outcome they are hoping for.
Go deeper
Spinoza's verdict
Baruch Spinoza considered the donkey in his Ethics and accepted the conclusion: a person placed in such perfect equilibrium, with nothing but hunger and thirst and the food and drink equidistant, would perish. He added that if asked whether such a person should be thought an ass rather than a man, he would not know what to say.
Related ideas
Further reading and sources
- EncyclopediaStanford Encyclopedia of Philosophy: John Buridan
- WikipediaBuridan's ass
- BookThe Incoherence of the Philosophers, Al-Ghazali
- BookEthics, Part II, Baruch Spinoza
Open questions
- Have you ever chosen between two things with no reason to prefer either? How?
- Does a choice need a reason to be free?
- Is a coin flip a decision?